Problem: Express this quotient in scientific notation: ${\frac{1.350\times 10^{-5}} {5.0\times 10^{-2}}}$
Solution: Start by collecting like terms together. $= {\frac{1.350} {5.0}} \times{\frac{10^{-5}} {10^{-2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.27 \times 10^{-5\,-\,-2}$ $= 0.27 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.27$ is the same as $2.70 \div 10$ , or $2.70 \times 10^{-1}$ $ = {2.70 \times 10^{-1}} \times 10^{-3} $ $= 2.70\times 10^{-4}$